The simple answer to your question is that the climax of this play takes place in Act III. For a more detailed examination, see below:
First, lets review the structure of plot, which consists of exposition (setting), rising action, climax, falling action, resolution, and denouement (best described as an epilogue).
In this play, as in most dramas of the time and many still today, breaks up the acts through the structure of the plot. Here, the prologue and first act are the exposition. They work to set up the characters and explain the conflict, as the men do in the opening of Act I. Act II is used to build the conflict and is, therefore, the rising action. Act III is when the climax occurs. The men we met in Act I, Fainall and Marwood, create their comedic plan to trick Lady Wishfort into giving her blessing to the marriage of Marwood and Mrs. Millamant. Act IV is the falling action as the plan is carried out, and Act V provides both the resolution and the denounement.